Figure REF  shows the inferred distribution of \(\chi _{\rm p}\)  as a function of different magnitude and tilt nodes, respectively. We also show the inferred distribution recovered from the Default model [1]}, [2]}, [3]}, [4]} analysis using the same event list, as well as the distribution corresponding to uniform distributions in \(a\)  and \(\cos \theta \) . The inferred distribution of \(\chi _{p}\)  is consistent with an isotropic distribution, and shows agreement with the \(\chi _{p}\)  distribution reconstructed from the Default model. An exception to this agreement is the slightly increased support at high \(\chi _{p}\)  that is not present in the Default reconstruction. The higher support for large \(a\)  and \(\cos (\theta ) \approx 0\)  in the spline model relative to the Default model may contribute to this increased support at high \(\chi _{p}\) . Similarly, our result allows for more support at high \(\chi _{p}\)  relative to what is presented in [2]}, in which it is assumed that the \(\chi _{\rm eff}\)  and \(\chi _{p}\)  distributions follow a multivariate normal distribution [6]}. In particular, Figure 16 in [2]} shows vanishing support for \(\chi _{p} > 0.4\)  in the population, whereas we find some support in this region is included at the 90% credibility.
We note that varying the number of nodes in spin magnitude has the largest impact on the averaged recovered \(\chi _{p}\)  distribution (dash-dotted curves) indicating that this measurement depends on our choice of prior for the spin magnitude distribution.
